The 26-year-old left-hander has been largely criticised in all quarters for attacking young England batsman Joe Root at a Birmingham bar in the early hours of Sunday morning. Cricket Australia have reacted by banning Warner from all cricket until the first Ashes Test against England begins at Trent Bridge on July 10.
"The Australians have, on the surface, been quite harsh on him, I think," he said on Sky Sports News.
"It certainly rules him out of the first couple of Test matches of the Ashes series so he'll be quite distraught to be missing out on that opportunity. But he's put himself in that situation and I suppose he's got to pay the price for it."
Strauss, who retired from all forms of cricket last year following England's Test series defeat against South Africa, stressed that Australia's management team need to take some of the responsibility.
"The individuals, for starters, I think are at fault on this but then the management, it's their job to make sure they keep everyone on the straight and narrow," he added.
"You have to have an environment where people know what's expected of them and what's not. It looks like Australia are going through that process at the moment trying to establish a line in the sand, some barriers there that players can't step out of. But unfortunately the players are testing those barriers at the moment."
Strauss' comments come after CA chief executive officer James Sutherland warned Warner that his actions have left his international career in the balance. Warner, who at a media conference on Thursday issued an apology, was also recently fined and warned over his future conduct by the governing body for becoming embroiled in a heated argument with two Australian journalists on Twitter.
Sutherland told a press conference in Brisbane: "Warner's specific indiscretion is entirely inappropriate, there is no place for violence anywhere and I'm extremely disappointed in that, I'm extremely disappointed in him and I have told him that.
"In regard to David Warner himself, I hope this is a turning point for him. I note that overnight he's made comments apologising for what he's done and expressing remorse for his actions. That's all well and good, it counts for a little bit but not much. What really counts is his actions going forward in the future and we're watching those very closely."